The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  X  1  1  1  1  X X^2  1  1  1  1 X^2 X^2+X X^2+X X^2+X  0  1  1  X  0 X^2+X  1  X  1  1
 0  1  1 X^2+X X^2+X+1  1 X^2 X+1  1  1 X^2+1  X X^2+X+1 X^2  1  1  X  1 X^2+X+1 X^2  1  1  1  1  1  0  0  1  1  1 X^2+X+1  1 X+1  0
 0  0  X  0 X^2+X  0  X X^2 X^2+X  X X^2  X X^2+X  X  X X^2+X  X  X X^2  0  0 X^2+X  0 X^2  0  0 X^2  0 X^2  0  X X^2+X X^2  0
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+82x^29+134x^30+214x^31+168x^32+356x^33+195x^34+352x^35+136x^36+196x^37+106x^38+64x^39+14x^40+4x^41+12x^42+8x^43+2x^45+2x^47+1x^48+1x^50

The gray image is a linear code over GF(2) with n=136, k=11 and d=58.
This code was found by Heurico 1.16 in 1.72 seconds.